84.8.11 problem 4.18 (c)

Internal problem ID [22123]
Book : Schaums outline series. Differential Equations By Richard Bronson. 1973. McGraw-Hill Inc. ISBN 0-07-008009-7
Section : Chapter 4. Separable first-order differential equations. Supplementary problems
Problem number : 4.18 (c)
Date solved : Thursday, October 02, 2025 at 08:25:36 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {x^{2} y-y}{1+y} \end{align*}

With initial conditions

\begin{align*} y \left (3\right )&=-1 \\ \end{align*}

✓ Maple. Time used: 0.162 (sec). Leaf size: 18

ode:=diff(y(x),x) = (x^2*y(x)-y(x))/(1+y(x)); 
ic:=[y(3) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \operatorname {LambertW}\left (-{\mathrm e}^{\frac {1}{3} x^{3}-x -7}\right ) \]

✓ Mathematica. Time used: 0.925 (sec). Leaf size: 22

ode=D[y[x],x]==(x^2*y[x]-y[x])/(1+y[x]); 
ic={y[3]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to W\left (-e^{\frac {x^3}{3}-x-7}\right ) \end{align*}

✓ Sympy. Time used: 2.546 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(x**2*y(x) - y(x))/(y(x) + 1) + Derivative(y(x), x),0) 
ics = {y(3): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = W\left (\frac {\sqrt [3]{- e^{x \left (x^{2} - 3\right )}} \left (-1 + \sqrt {3} i\right )}{2 e^{7}}\right ) \]